SYZ for Hypersurfaces of Toric Fano Manifolds and Optimal Transport - Part 1

Explore a 58-minute lecture on the SYZ-conjecture in mirror symmetry, focusing on Calabi-Yau hypersurfaces in toric Fano manifolds. Delve into Yang Li's work that reduces a weak version of the SYZ-conjecture to solving a real Monge-Ampère equation on polytope boundaries. Learn about the intriguing relationship between equation solvability and optimal transport theory, while understanding how the discriminant locus's location becomes clearer through this theoretical framework. Discover the collaborative research findings with Rolf Andreasson, Mattias Jonsson, Enrica Mazzon, and Nick McCleerey, examining both solved aspects and remaining open problems in this mathematical domain.